From March 1960 to October 1967 Menadue was private secretary to Gough Whitlam, deputy leader of the Labor Opposition in the federal parliament (Whitlam became leader in February 1967). In 1966 Menadue stood unsuccessfully as Labor candidate for the NSW federal seat of Hume.[3] After leaving Whitlam's employ, he moved into the private sector for seven years as general manager at News Limited, publisher of The Australian.

Menadue was Chief Executive Officer of Qantas from June 1986 to July 1989. He was a Director of Telstra from December 1994 to October 1996, a Director of NSW State Rail Authority from 1996 to 1999, and Chairman of the Australia Japan Foundation from 1991 to 1998.

Menadue is an adviser to several companies. He chaired the NSW Health Council, which reported to the NSW Minister for Health in March 2000 on changes to health services in NSW. He also chaired the SA Generational Health Review which reported to the South Australian Minister for Human Services in May 2003.

In October 1999, Menadue published his autobiography Things You Learn Along the Way.[5] He was the founding Chair of New Matilda (NewMatilda.com), an independent weekly online newsletter which was launched in August 2004. He is the founder and fellow of public-interest think tank, the Centre for Policy Development.[6] He also publishes the public affairs blogsite Pearls and Irritations.[7]